Abstract About 12 billion years ago, the Universe was first experiencing light again after the dark ages, and galaxies filled the environment with stars, metals, and dust. How efficient was this process? How fast did these primordial galaxies form stars and dust? We can answer these questions by tracing the star formation rate density (SFRD) back to its widely unknown high-redshift tail, traditionally observed in the near-infrared (NIR), optical, and UV bands. Thus, objects with a large amount of dust were missing. We aim to fill this knowledge gap by studying radio-selected NIR-dark (RS-NIRdark) sources, i.e., sources not having a counterpart at UV-to-NIR wavelengths. We widen the sample of Talia et al. from 197 to 272 objects in the Cosmic Evolution Survey (COSMOS) field, including also photometrically contaminated sources, which were previously excluded. Another important step forward consists in the visual inspection of each source in the bands from u* to MIPS 24 μm. According to their “environment” in the different bands, we are able to highlight different cases of study and calibrate an appropriate photometric procedure for the objects affected by confusion issues. We estimate that the contribution of RS-NIRdark sources to the cosmic SFRD at 3 < z < 5 is ∼10%–25% of that based on UV-selected galaxies.